LMFDB - Embedded newform 230.6.b.a.139.23

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,6,Mod(139,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("230.139"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	230.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [26] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$36.8882785570$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.23
Character	$\chi$	$=$	230.139
Dual form			230.6.b.a.139.4

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+4.00000i q^{2} +13.9839i q^{3} -16.0000 q^{4} +(-7.76744 + 55.3594i) q^{5} -55.9357 q^{6} +114.735i q^{7} -64.0000i q^{8} +47.4501 q^{9} +(-221.438 - 31.0698i) q^{10} -208.757 q^{11} -223.743i q^{12} +757.151i q^{13} -458.938 q^{14} +(-774.142 - 108.619i) q^{15} +256.000 q^{16} +1028.75i q^{17} +189.800i q^{18} -1923.29 q^{19} +(124.279 - 885.751i) q^{20} -1604.44 q^{21} -835.026i q^{22} +529.000i q^{23} +894.971 q^{24} +(-3004.33 - 860.003i) q^{25} -3028.60 q^{26} +4061.63i q^{27} -1835.75i q^{28} +4599.22 q^{29} +(434.477 - 3096.57i) q^{30} +6063.57 q^{31} +1024.00i q^{32} -2919.23i q^{33} -4115.01 q^{34} +(-6351.64 - 891.194i) q^{35} -759.201 q^{36} -10846.8i q^{37} -7693.15i q^{38} -10587.9 q^{39} +(3543.00 + 497.116i) q^{40} -3496.19 q^{41} -6417.75i q^{42} +6231.87i q^{43} +3340.11 q^{44} +(-368.566 + 2626.81i) q^{45} -2116.00 q^{46} +3096.80i q^{47} +3579.88i q^{48} +3642.99 q^{49} +(3440.01 - 12017.3i) q^{50} -14386.0 q^{51} -12114.4i q^{52} -10267.9i q^{53} -16246.5 q^{54} +(1621.51 - 11556.6i) q^{55} +7343.01 q^{56} -26895.1i q^{57} +18396.9i q^{58} -5297.34 q^{59} +(12386.3 + 1737.91i) q^{60} +54433.0 q^{61} +24254.3i q^{62} +5444.16i q^{63} -4096.00 q^{64} +(-41915.5 - 5881.13i) q^{65} +11676.9 q^{66} -39973.0i q^{67} -16460.0i q^{68} -7397.49 q^{69} +(3564.78 - 25406.6i) q^{70} -4371.19 q^{71} -3036.80i q^{72} +25765.2i q^{73} +43387.2 q^{74} +(12026.2 - 42012.4i) q^{75} +30772.6 q^{76} -23951.6i q^{77} -42351.8i q^{78} +44456.9 q^{79} +(-1988.47 + 14172.0i) q^{80} -45267.1 q^{81} -13984.7i q^{82} -102141. i q^{83} +25671.0 q^{84} +(-56951.1 - 7990.77i) q^{85} -24927.5 q^{86} +64315.1i q^{87} +13360.4i q^{88} +113318. q^{89} +(-10507.2 - 1474.26i) q^{90} -86871.4 q^{91} -8464.00i q^{92} +84792.4i q^{93} -12387.2 q^{94} +(14939.0 - 106472. i) q^{95} -14319.5 q^{96} -10460.6i q^{97} +14571.9i q^{98} -9905.51 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 416 q^{4} - 30 q^{5} - 72 q^{6} - 1400 q^{9} + 80 q^{10} - 1314 q^{11} + 808 q^{14} + 1280 q^{15} + 6656 q^{16} + 6630 q^{19} + 480 q^{20} - 10060 q^{21} + 1152 q^{24} - 10470 q^{25} - 376 q^{26}+ \cdots + 523850 q^{99}+O(q^{100}) $ 26 * q - 416 * q^4 - 30 * q^5 - 72 * q^6 - 1400 * q^9 + 80 * q^10 - 1314 * q^11 + 808 * q^14 + 1280 * q^15 + 6656 * q^16 + 6630 * q^19 + 480 * q^20 - 10060 * q^21 + 1152 * q^24 - 10470 * q^25 - 376 * q^26 + 16084 * q^29 - 6200 * q^30 + 418 * q^31 + 3320 * q^34 - 3160 * q^35 + 22400 * q^36 + 71296 * q^39 - 1280 * q^40 - 35826 * q^41 + 21024 * q^44 - 83960 * q^45 - 55016 * q^46 + 53532 * q^49 - 20800 * q^50 - 25430 * q^51 + 98736 * q^54 - 110390 * q^55 - 12928 * q^56 + 126992 * q^59 - 20480 * q^60 - 63662 * q^61 - 106496 * q^64 - 88520 * q^65 - 18664 * q^66 - 9522 * q^69 - 116520 * q^70 - 106514 * q^71 + 183536 * q^74 - 44200 * q^75 - 106080 * q^76 + 324676 * q^79 - 7680 * q^80 - 170702 * q^81 + 160960 * q^84 + 120780 * q^85 - 42768 * q^86 + 465200 * q^89 + 61360 * q^90 - 468838 * q^91 + 107152 * q^94 + 309670 * q^95 - 18432 * q^96 + 523850 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			4.00000i			0.707107i
$2$			4.00000i			0.707107i
$3$			13.9839i			0.897069i	0.893766	+	0.448534i	$0.148054\pi$
$3$			13.9839i			0.897069i	−0.893766	+	0.448534i	$0.851946\pi$
$4$	−16.0000			−0.500000
$5$	−7.76744	+	55.3594i	−0.138948	+	0.990300i
$5$	−7.76744	+	55.3594i	−0.138948	+	0.990300i
$6$	−55.9357			−0.634323
$7$			114.735i			0.885012i	0.896766	+	0.442506i	$0.145910\pi$
$7$			114.735i			0.885012i	−0.896766	+	0.442506i	$0.854090\pi$
$8$		−	64.0000i		−	0.353553i
$9$	47.4501			0.195268
$10$	−221.438	−	31.0698i	−0.700248	−	0.0982513i
$11$	−208.757			−0.520186			−0.260093	−	0.965584i	$-0.583753\pi$
$11$	−208.757			−0.520186			−0.260093	+	0.965584i	$0.583753\pi$
$12$		−	223.743i		−	0.448534i
$13$			757.151i			1.24258i	0.783581	+	0.621290i	$0.213391\pi$
$13$			757.151i			1.24258i	−0.783581	+	0.621290i	$0.786609\pi$
$14$	−458.938			−0.625798
$15$	−774.142	−	108.619i	−0.888367	−	0.124646i
$16$	256.000			0.250000
$17$			1028.75i			0.863353i	0.902028	+	0.431677i	$0.142078\pi$
$17$			1028.75i			0.863353i	−0.902028	+	0.431677i	$0.857922\pi$
$18$			189.800i			0.138075i
$19$	−1923.29			−1.22225			−0.611126	−	0.791534i	$-0.709283\pi$
$19$	−1923.29			−1.22225			−0.611126	+	0.791534i	$0.709283\pi$
$20$	124.279	−	885.751i	0.0694741	−	0.495150i
$21$	−1604.44			−0.793916
$22$		−	835.026i		−	0.367827i
$23$			529.000i			0.208514i
$23$			529.000i			0.208514i
$24$	894.971			0.317162
$25$	−3004.33	−	860.003i	−0.961387	−	0.275201i
$26$	−3028.60			−0.878636
$27$			4061.63i			1.07224i
$28$		−	1835.75i		−	0.442506i
$29$	4599.22			1.01552			0.507761	−	0.861498i	$-0.330473\pi$
$29$	4599.22			1.01552			0.507761	+	0.861498i	$0.330473\pi$
$30$	434.477	−	3096.57i	0.0881381	−	0.628170i
$31$	6063.57			1.13325			0.566623	−	0.823977i	$-0.308250\pi$
$31$	6063.57			1.13325			0.566623	+	0.823977i	$0.308250\pi$
$32$			1024.00i			0.176777i
$33$		−	2919.23i		−	0.466642i
$34$	−4115.01			−0.610483
$35$	−6351.64	−	891.194i	−0.876427	−	0.122971i
$36$	−759.201			−0.0976339
$37$		−	10846.8i		−	1.30256i	−0.758839	−	0.651279i	$-0.774233\pi$
$37$		−	10846.8i		−	1.30256i	0.758839	−	0.651279i	$-0.225767\pi$
$38$		−	7693.15i		−	0.864262i
$39$	−10587.9			−1.11468
$40$	3543.00	+	497.116i	0.350124	+	0.0491256i
$41$	−3496.19			−0.324814			−0.162407	−	0.986724i	$-0.551926\pi$
$41$	−3496.19			−0.324814			−0.162407	+	0.986724i	$0.551926\pi$
$42$		−	6417.75i		−	0.561384i
$43$			6231.87i			0.513982i	0.966414	+	0.256991i	$0.0827310\pi$
$43$			6231.87i			0.513982i	−0.966414	+	0.256991i	$0.917269\pi$
$44$	3340.11			0.260093
$45$	−368.566	+	2626.81i	−0.0271321	+	0.193374i
$46$	−2116.00			−0.147442
$47$			3096.80i			0.204488i	0.994759	+	0.102244i	$0.0326023\pi$
$47$			3096.80i			0.204488i	−0.994759	+	0.102244i	$0.967398\pi$
$48$			3579.88i			0.224267i
$49$	3642.99			0.216754
$50$	3440.01	−	12017.3i	0.194596	−	0.679803i
$51$	−14386.0			−0.774487
$52$		−	12114.4i		−	0.621290i
$53$		−	10267.9i		−	0.502102i	−0.967974	−	0.251051i	$-0.919224\pi$
$53$		−	10267.9i		−	0.502102i	0.967974	−	0.251051i	$-0.0807762\pi$
$54$	−16246.5			−0.758186
$55$	1621.51	−	11556.6i	0.0722789	−	0.515140i
$56$	7343.01			0.312899
$57$		−	26895.1i		−	1.09644i
$58$			18396.9i			0.718082i
$59$	−5297.34			−0.198120			−0.0990599	−	0.995081i	$-0.531584\pi$
$59$	−5297.34			−0.198120			−0.0990599	+	0.995081i	$0.531584\pi$
$60$	12386.3	+	1737.91i	0.444183	+	0.0623231i
$61$	54433.0			1.87300			0.936500	−	0.350667i	$-0.114045\pi$
$61$	54433.0			1.87300			0.936500	+	0.350667i	$0.114045\pi$
$62$			24254.3i			0.801326i
$63$			5444.16i			0.172814i
$64$	−4096.00			−0.125000
$65$	−41915.5	−	5881.13i	−1.23053	−	0.172654i
$66$	11676.9			0.329966
$67$		−	39973.0i		−	1.08788i	−0.839125	−	0.543938i	$-0.816933\pi$
$67$		−	39973.0i		−	1.08788i	0.839125	−	0.543938i	$-0.183067\pi$
$68$		−	16460.0i		−	0.431677i
$69$	−7397.49			−0.187052
$70$	3564.78	−	25406.6i	0.0869535	−	0.619727i
$71$	−4371.19			−0.102909			−0.0514546	−	0.998675i	$-0.516386\pi$
$71$	−4371.19			−0.102909			−0.0514546	+	0.998675i	$0.516386\pi$
$72$		−	3036.80i		−	0.0690376i
$73$			25765.2i			0.565882i	0.959137	+	0.282941i	$0.0913101\pi$
$73$			25765.2i			0.565882i	−0.959137	+	0.282941i	$0.908690\pi$
$74$	43387.2			0.921047
$75$	12026.2	−	42012.4i	0.246874	−	0.862430i
$76$	30772.6			0.611126
$77$		−	23951.6i		−	0.460371i
$78$		−	42351.8i		−	0.788197i
$79$	44456.9			0.801441			0.400721	−	0.916200i	$-0.368760\pi$
$79$	44456.9			0.801441			0.400721	+	0.916200i	$0.368760\pi$
$80$	−1988.47	+	14172.0i	−0.0347371	+	0.247575i
$81$	−45267.1			−0.766603
$82$		−	13984.7i		−	0.229678i
$83$		−	102141.i		−	1.62743i	−0.581261	−	0.813717i	$-0.697440\pi$
$83$		−	102141.i		−	1.62743i	0.581261	−	0.813717i	$-0.302560\pi$
$84$	25671.0			0.396958
$85$	−56951.1	−	7990.77i	−0.854978	−	0.119961i
$86$	−24927.5			−0.363440
$87$			64315.1i			0.910993i
$88$			13360.4i			0.183913i
$89$	113318.			1.51643			0.758215	−	0.652005i	$-0.226072\pi$
$89$	113318.			1.51643			0.758215	+	0.652005i	$0.226072\pi$
$90$	−10507.2	−	1474.26i	−0.136736	−	0.0191853i
$91$	−86871.4			−1.09970
$92$		−	8464.00i		−	0.104257i
$93$			84792.4i			1.01660i
$94$	−12387.2			−0.144595
$95$	14939.0	−	106472.i	0.169830	−	1.21039i
$96$	−14319.5			−0.158581
$97$		−	10460.6i		−	0.112882i	−0.998406	−	0.0564411i	$-0.982025\pi$
$97$		−	10460.6i		−	0.112882i	0.998406	−	0.0564411i	$-0.0179753\pi$
$98$			14571.9i			0.153268i
$99$	−9905.51			−0.101576
$100$	48069.3	+	13760.0i	0.480693	+	0.137600i
$101$	−125463.			−1.22381			−0.611904	−	0.790932i	$-0.709596\pi$
$101$	−125463.			−1.22381			−0.611904	+	0.790932i	$0.709596\pi$
$102$		−	57543.9i		−	0.547645i
$103$		−	141707.i		−	1.31613i	−0.752961	−	0.658065i	$-0.771375\pi$
$103$		−	141707.i		−	1.31613i	0.752961	−	0.658065i	$-0.228625\pi$
$104$	48457.7			0.439318
$105$	12462.4	−	88820.8i	0.110313	−	0.786215i
$106$	41071.6			0.355040
$107$			136989.i			1.15671i	0.815785	+	0.578356i	$0.196305\pi$
$107$			136989.i			1.15671i	−0.815785	+	0.578356i	$0.803695\pi$
$108$		−	64986.1i		−	0.536119i
$109$	−120603.			−0.972283			−0.486141	−	0.873880i	$-0.661596\pi$
$109$	−120603.			−0.972283			−0.486141	+	0.873880i	$0.661596\pi$
$110$	46226.6	+	6486.02i	0.364259	+	0.0511089i
$111$	151681.			1.16848
$112$			29372.0i			0.221253i
$113$			217455.i			1.60204i	0.598637	+	0.801021i	$0.295709\pi$
$113$			217455.i			1.60204i	−0.598637	+	0.801021i	$0.704291\pi$
$114$	107580.			0.775302
$115$	−29285.1	−	4108.98i	−0.206492	−	0.0289727i
$116$	−73587.5			−0.507761
$117$			35926.9i			0.242636i
$118$		−	21189.4i		−	0.140092i
$119$	−118033.			−0.764078
$120$	−6951.63	+	49545.1i	−0.0440691	+	0.314085i
$121$	−117472.			−0.729407
$122$			217732.i			1.32441i
$123$		−	48890.4i		−	0.291381i
$124$	−97017.1			−0.566623
$125$	70945.3	−	159638.i	0.406114	−	0.913822i
$126$	−21776.6			−0.122198
$127$			151854.i			0.835444i	0.908575	+	0.417722i	$0.137171\pi$
$127$			151854.i			0.835444i	−0.908575	+	0.417722i	$0.862829\pi$
$128$		−	16384.0i		−	0.0883883i
$129$	−87146.0			−0.461077
$130$	23524.5	−	167662.i	0.122085	−	0.870113i
$131$	27895.6			0.142023			0.0710114	−	0.997476i	$-0.477377\pi$
$131$	27895.6			0.142023			0.0710114	+	0.997476i	$0.477377\pi$
$132$			46707.8i			0.233321i
$133$		−	220668.i		−	1.08171i
$134$	159892.			0.769245
$135$	−224850.	−	31548.5i	−1.06184	−	0.148986i
$136$	65840.1			0.305241
$137$		−	107380.i		−	0.488790i	−0.969676	−	0.244395i	$-0.921411\pi$
$137$		−	107380.i		−	0.488790i	0.969676	−	0.244395i	$-0.0785893\pi$
$138$		−	29590.0i		−	0.132266i
$139$	−191263.			−0.839642			−0.419821	−	0.907607i	$-0.637907\pi$
$139$	−191263.			−0.839642			−0.419821	+	0.907607i	$0.637907\pi$
$140$	101626.	+	14259.1i	0.438213	+	0.0614854i
$141$	−43305.4			−0.183440
$142$		−	17484.8i		−	0.0727678i
$143$		−	158060.i		−	0.646372i
$144$	12147.2			0.0488169
$145$	−35724.2	+	254610.i	−0.141105	+	1.00567i
$146$	−103061.			−0.400139
$147$			50943.2i			0.194443i
$148$			173549.i			0.651279i
$149$	370689.			1.36787			0.683934	−	0.729544i	$-0.260268\pi$
$149$	370689.			1.36787			0.683934	+	0.729544i	$0.260268\pi$
$150$	168049.	+	48104.8i	0.609830	+	0.174566i
$151$	−292983.			−1.04568			−0.522841	−	0.852430i	$-0.675128\pi$
$151$	−292983.			−1.04568			−0.522841	+	0.852430i	$0.675128\pi$
$152$			123090.i			0.432131i
$153$			48814.4i			0.168585i
$154$	95806.4			0.325531
$155$	−47098.4	+	335676.i	−0.157463	+	1.12225i
$156$	169407.			0.557340
$157$			380286.i			1.23129i	0.788023	+	0.615646i	$0.211105\pi$
$157$			380286.i			1.23129i	−0.788023	+	0.615646i	$0.788895\pi$
$158$			177828.i			0.566705i
$159$	143585.			0.450420
$160$	−56688.1	−	7953.86i	−0.175062	−	0.0245628i
$161$	−60694.6			−0.184538
$162$		−	181068.i		−	0.542070i
$163$			515812.i			1.52062i	0.649558	+	0.760312i	$0.274954\pi$
$163$			515812.i			1.52062i	−0.649558	+	0.760312i	$0.725046\pi$
$164$	55939.0			0.162407
$165$	161607.	+	22675.0i	0.462116	+	0.0648392i
$166$	408563.			1.15077
$167$			376329.i			1.04418i	0.852890	+	0.522091i	$0.174848\pi$
$167$			376329.i			1.04418i	−0.852890	+	0.522091i	$0.825152\pi$
$168$			102684.i			0.280692i
$169$	−201985.			−0.544004
$170$	31963.1	−	227805.i	0.0848255	−	0.604561i
$171$	−91260.2			−0.238666
$172$		−	99710.0i		−	0.256991i
$173$			20689.1i			0.0525564i	0.999655	+	0.0262782i	$0.00836558\pi$
$173$			20689.1i			0.0525564i	−0.999655	+	0.0262782i	$0.991634\pi$
$174$	−257260.			−0.644169
$175$	98672.0	−	344701.i	0.243556	−	0.850839i
$176$	−53441.7			−0.130046
$177$		−	74077.6i		−	0.177727i
$178$			453270.i			1.07228i
$179$	334571.			0.780470			0.390235	−	0.920715i	$-0.372394\pi$
$179$	334571.			0.780470			0.390235	+	0.920715i	$0.372394\pi$
$180$	5897.05	−	42028.9i	0.0135661	−	0.0966868i
$181$	−725066.			−1.64506			−0.822529	−	0.568723i	$-0.807438\pi$
$181$	−725066.			−1.64506			−0.822529	+	0.568723i	$0.807438\pi$
$182$		−	347486.i		−	0.777604i
$183$			761187.i			1.68021i
$184$	33856.0			0.0737210
$185$	600472.	+	84251.8i	1.28992	+	0.180988i
$186$	−339170.			−0.718844
$187$		−	214759.i		−	0.449104i
$188$		−	49548.8i		−	0.102244i
$189$	−466009.			−0.948943
$190$	425889.	+	59756.1i	0.855878	+	0.120088i
$191$	−443518.			−0.879687			−0.439844	−	0.898074i	$-0.644966\pi$
$191$	−443518.			−0.879687			−0.439844	+	0.898074i	$0.644966\pi$
$192$		−	57278.1i		−	0.112134i
$193$			811440.i			1.56806i	0.620721	+	0.784031i	$0.286840\pi$
$193$			811440.i			1.56806i	−0.620721	+	0.784031i	$0.713160\pi$
$194$	41842.3			0.0798198
$195$	82241.2	−	586142.i	0.154883	−	1.10387i
$196$	−58287.8			−0.108377
$197$		−	251172.i		−	0.461111i	−0.973059	−	0.230555i	$-0.925946\pi$
$197$		−	251172.i		−	0.461111i	0.973059	−	0.230555i	$-0.0740543\pi$
$198$		−	39622.1i		−	0.0718247i
$199$	313383.			0.560973			0.280487	−	0.959858i	$-0.409504\pi$
$199$	313383.			0.560973			0.280487	+	0.959858i	$0.409504\pi$
$200$	−55040.2	+	192277.i	−0.0972982	+	0.339902i
$201$	558979.			0.975900
$202$		−	501853.i		−	0.865362i
$203$			527689.i			0.898748i
$204$	230176.			0.387244
$205$	27156.4	−	193547.i	0.0451324	−	0.321663i
$206$	566829.			0.930645
$207$			25101.1i			0.0407161i
$208$			193831.i			0.310645i
$209$	401499.			0.635798
$210$	355283.	+	49849.5i	0.555938	+	0.0780033i
$211$	−275717.			−0.426341			−0.213170	−	0.977015i	$-0.568379\pi$
$211$	−275717.			−0.426341			−0.213170	+	0.977015i	$0.568379\pi$
$212$			164286.i			0.251051i
$213$		−	61126.4i		−	0.0923166i
$214$	−547955.			−0.817919
$215$	−344993.	−	48405.7i	−0.508996	−	0.0714169i
$216$	259944.			0.379093
$217$			695701.i			1.00294i
$218$		−	482413.i		−	0.687508i
$219$	−360298.			−0.507635
$220$	−25944.1	+	184906.i	−0.0361395	+	0.257570i
$221$	−778921.			−1.07278
$222$			606722.i			0.826243i
$223$		−	67438.0i		−	0.0908118i	−0.998969	−	0.0454059i	$-0.985542\pi$
$223$		−	67438.0i		−	0.0908118i	0.998969	−	0.0454059i	$-0.0144581\pi$
$224$	−117488.			−0.156449
$225$	−142556.	−	40807.2i	−0.187728	−	0.0537379i
$226$	−869821.			−1.13281
$227$		−	1.05463e6i		−	1.35842i	−0.733944	−	0.679210i	$-0.762323\pi$
$227$		−	1.05463e6i		−	1.35842i	0.733944	−	0.679210i	$-0.237677\pi$
$228$			430322.i			0.548222i
$229$	251989.			0.317535			0.158768	−	0.987316i	$-0.449248\pi$
$229$	251989.			0.317535			0.158768	+	0.987316i	$0.449248\pi$
$230$	16435.9	−	117141.i	0.0204868	−	0.146012i
$231$	334937.			0.412984
$232$		−	294350.i		−	0.359041i
$233$			273022.i			0.329464i	0.986338	+	0.164732i	$0.0526760\pi$
$233$			273022.i			0.329464i	−0.986338	+	0.164732i	$0.947324\pi$
$234$	−143708.			−0.171569
$235$	−171437.	−	24054.2i	−0.202505	−	0.0284133i
$236$	84757.5			0.0990599
$237$			621682.i			0.718948i
$238$		−	472134.i		−	0.540284i
$239$	−578971.			−0.655635			−0.327817	−	0.944741i	$-0.606313\pi$
$239$	−578971.			−0.655635			−0.327817	+	0.944741i	$0.606313\pi$
$240$	−198180.	−	27806.5i	−0.222092	−	0.0311615i
$241$	−602684.			−0.668417			−0.334208	−	0.942499i	$-0.608469\pi$
$241$	−602684.			−0.668417			−0.334208	+	0.942499i	$0.608469\pi$
$242$		−	469887.i		−	0.515768i
$243$			353964.i			0.384542i
$244$	−870928.			−0.936500
$245$	−28296.7	+	201674.i	−0.0301176	+	0.214652i
$246$	195561.			0.206037
$247$		−	1.45622e6i		−	1.51874i
$248$		−	388068.i		−	0.400663i
$249$	1.42833e6			1.45992
$250$	638553.	+	283781.i	0.646170	+	0.287166i
$251$	−407710.			−0.408477			−0.204238	−	0.978921i	$-0.565472\pi$
$251$	−407710.			−0.408477			−0.204238	+	0.978921i	$0.565472\pi$
$252$		−	87106.6i		−	0.0864071i
$253$		−	110432.i		−	0.108466i
$254$	−607416.			−0.590748
$255$	111742.	−	796400.i	0.107614	−	0.766974i
$256$	65536.0			0.0625000
$257$			117364.i			0.110841i	0.998463	+	0.0554205i	$0.0176499\pi$
$257$			117364.i			0.110841i	−0.998463	+	0.0554205i	$0.982350\pi$
$258$		−	348584.i		−	0.326031i
$259$	1.24450e6			1.15278
$260$	670647.	+	94098.1i	0.615263	+	0.0863271i
$261$	218233.			0.198299
$262$			111583.i			0.100425i
$263$		−	937112.i		−	0.835414i	−0.908582	−	0.417707i	$-0.862834\pi$
$263$		−	937112.i		−	0.835414i	0.908582	−	0.417707i	$-0.137166\pi$
$264$	−186831.			−0.164983
$265$	568425.	+	79755.3i	0.497231	+	0.0697662i
$266$	882670.			0.764882
$267$			1.58462e6i			1.36034i
$268$			639568.i			0.543938i
$269$	1.61988e6			1.36490			0.682451	−	0.730932i	$-0.260914\pi$
$269$	1.61988e6			1.36490			0.682451	+	0.730932i	$0.260914\pi$
$270$	126194.	−	899398.i	0.105349	−	0.750832i
$271$	−1.28949e6			−1.06659			−0.533293	−	0.845931i	$-0.679046\pi$
$271$	−1.28949e6			−1.06659			−0.533293	+	0.845931i	$0.679046\pi$
$272$			263361.i			0.215838i
$273$		−	1.21480e6i		−	0.986504i
$274$	429520.			0.345627
$275$	627174.	+	179531.i	0.500100	+	0.143156i
$276$	118360.			0.0935259
$277$		−	632037.i		−	0.494929i	−0.968897	−	0.247464i	$-0.920403\pi$
$277$		−	632037.i		−	0.494929i	0.968897	−	0.247464i	$-0.0795973\pi$
$278$		−	765052.i		−	0.593716i
$279$	287717.			0.221286
$280$	−57036.4	+	406505.i	−0.0434768	+	0.309864i
$281$	417873.			0.315703			0.157851	−	0.987463i	$-0.449543\pi$
$281$	417873.			0.315703			0.157851	+	0.987463i	$0.449543\pi$
$282$		−	173221.i		−	0.129712i
$283$		−	84357.4i		−	0.0626119i	−0.999510	−	0.0313059i	$-0.990033\pi$
$283$		−	84357.4i		−	0.0626119i	0.999510	−	0.0313059i	$-0.00996662\pi$
$284$	69939.1			0.0514546
$285$	1.48890e6	+	208906.i	1.08581	+	0.152349i
$286$	632241.			0.457054
$287$		−	401133.i		−	0.287464i
$288$			48588.9i			0.0345188i
$289$	361526.			0.254621
$290$	−1.01844e6	−	142897.i	−0.711116	−	0.0997763i
$291$	146280.			0.101263
$292$		−	412243.i		−	0.282941i
$293$			1.15866e6i			0.788474i	0.919009	+	0.394237i	$0.128991\pi$
$293$			1.15866e6i			0.788474i	−0.919009	+	0.394237i	$0.871009\pi$
$294$	−203773.			−0.137492
$295$	41146.8	−	293258.i	0.0275284	−	0.196198i
$296$	−694195.			−0.460524
$297$		−	847892.i		−	0.557763i
$298$			1.48276e6i			0.967229i
$299$	−400533.			−0.259096
$300$	−192419.	+	672198.i	−0.123437	+	0.431215i
$301$	−715011.			−0.454880
$302$		−	1.17193e6i		−	0.739409i
$303$		−	1.75447e6i		−	1.09784i
$304$	−492362.			−0.305563
$305$	−422805.	+	3.01338e6i	−0.260250	+	1.85483i
$306$	−195257.			−0.119208
$307$		−	2.83360e6i		−	1.71590i	−0.513729	−	0.857952i	$-0.671736\pi$
$307$		−	2.83360e6i		−	1.71590i	0.513729	−	0.857952i	$-0.328264\pi$
$308$			383225.i			0.230185i
$309$	1.98162e6			1.18066
$310$	−1.34270e6	−	188394.i	−0.793553	−	0.111343i
$311$	508595.			0.298175			0.149087	−	0.988824i	$-0.452366\pi$
$311$	508595.			0.298175			0.149087	+	0.988824i	$0.452366\pi$
$312$			677628.i			0.394099i
$313$		−	1.07973e6i		−	0.622949i	−0.950255	−	0.311475i	$-0.899177\pi$
$313$		−	1.07973e6i		−	0.622949i	0.950255	−	0.311475i	$-0.100823\pi$
$314$	−1.52114e6			−0.870655
$315$	−301386.	−	42287.2i	−0.171138	−	0.0240122i
$316$	−711311.			−0.400721
$317$		−	3.17514e6i		−	1.77466i	−0.461139	−	0.887328i	$-0.652559\pi$
$317$		−	3.17514e6i		−	1.77466i	0.461139	−	0.887328i	$-0.347441\pi$
$318$			574342.i			0.318495i
$319$	−960117.			−0.528260
$320$	31815.5	−	226752.i	0.0173685	−	0.123787i
$321$	−1.91564e6			−1.03765
$322$		−	242778.i		−	0.130488i
$323$		−	1.97859e6i		−	1.05523i
$324$	724274.			0.383301
$325$	651152.	−	2.27473e6i	0.341959	−	1.19460i
$326$	−2.06325e6			−1.07524
$327$		−	1.68650e6i		−	0.872204i
$328$			223756.i			0.114839i
$329$	−355310.			−0.180974
$330$	−90700.0	+	646429.i	−0.0458482	+	0.326765i
$331$	−3.29231e6			−1.65170			−0.825850	−	0.563890i	$-0.809304\pi$
$331$	−3.29231e6			−1.65170			−0.825850	+	0.563890i	$0.809304\pi$
$332$			1.63425e6i			0.813717i
$333$		−	514681.i		−	0.254348i
$334$	−1.50532e6			−0.738349
$335$	2.21288e6	+	310488.i	1.07732	+	0.151158i
$336$	−410736.			−0.198479
$337$			3.44514e6i			1.65246i	0.563330	+	0.826232i	$0.309520\pi$
$337$			3.44514e6i			1.65246i	−0.563330	+	0.826232i	$0.690480\pi$
$338$		−	807940.i		−	0.384669i
$339$	−3.04088e6			−1.43714
$340$	911218.	+	127852.i	0.427489	+	0.0599807i
$341$	−1.26581e6			−0.589498
$342$		−	365041.i		−	0.168763i
$343$			2.34632e6i			1.07684i
$344$	398840.			0.181720
$345$	57459.6	−	409521.i	0.0259905	−	0.185237i
$346$	−82756.3			−0.0371630
$347$		−	1.26186e6i		−	0.562586i	−0.959622	−	0.281293i	$-0.909237\pi$
$347$		−	1.26186e6i		−	0.562586i	0.959622	−	0.281293i	$-0.0907632\pi$
$348$		−	1.02904e6i		−	0.455496i
$349$	2.59689e6			1.14127			0.570636	−	0.821203i	$-0.306697\pi$
$349$	2.59689e6			1.14127			0.570636	+	0.821203i	$0.306697\pi$
$350$	1.37880e6	+	394688.i	0.601634	+	0.172220i
$351$	−3.07527e6			−1.33234
$352$		−	213767.i		−	0.0919567i
$353$		−	1.24536e6i		−	0.531932i	−0.963982	−	0.265966i	$-0.914309\pi$
$353$		−	1.24536e6i		−	0.531932i	0.963982	−	0.265966i	$-0.0856910\pi$
$354$	296310.			0.125672
$355$	33953.0	−	241987.i	0.0142991	−	0.101911i
$356$	−1.81308e6			−0.758215
$357$		−	1.65057e6i		−	0.685430i
$358$			1.33829e6i			0.551875i
$359$	−262815.			−0.107625			−0.0538126	−	0.998551i	$-0.517137\pi$
$359$	−262815.			−0.107625			−0.0538126	+	0.998551i	$0.517137\pi$
$360$	168116.	+	23588.2i	0.0683679	+	0.00959265i
$361$	1.22294e6			0.493898
$362$		−	2.90026e6i		−	1.16323i
$363$		−	1.64271e6i		−	0.654328i
$364$	1.38994e6			0.549849
$365$	−1.42635e6	−	200130.i	−0.560393	−	0.0786284i
$366$	−3.04475e6			−1.18809
$367$			4.01045e6i			1.55428i	0.629331	+	0.777138i	$0.283329\pi$
$367$			4.01045e6i			1.55428i	−0.629331	+	0.777138i	$0.716671\pi$
$368$			135424.i			0.0521286i
$369$	−165894.			−0.0634257
$370$	−337007.	+	2.40189e6i	−0.127978	+	0.912113i
$371$	1.17808e6			0.444366
$372$		−	1.35668e6i		−	0.508300i
$373$		−	1.29316e6i		−	0.481261i	−0.970617	−	0.240630i	$-0.922646\pi$
$373$		−	1.29316e6i		−	0.481261i	0.970617	−	0.240630i	$-0.0773541\pi$
$374$	859035.			0.317564
$375$	2.23237e6	+	992092.i	0.819761	+	0.364312i
$376$	198195.			0.0722975
$377$			3.48230e6i			1.26187i
$378$		−	1.86404e6i		−	0.671004i
$379$	−266332.			−0.0952414			−0.0476207	−	0.998865i	$-0.515164\pi$
$379$	−266332.			−0.0952414			−0.0476207	+	0.998865i	$0.515164\pi$
$380$	−239025.	+	1.70355e6i	−0.0849148	+	0.605197i
$381$	−2.12352e6			−0.749450
$382$		−	1.77407e6i		−	0.622033i
$383$		−	3.70896e6i		−	1.29198i	−0.763346	−	0.645989i	$-0.776445\pi$
$383$		−	3.70896e6i		−	1.29198i	0.763346	−	0.645989i	$-0.223555\pi$
$384$	229112.			0.0792904
$385$	1.32595e6	+	186043.i	0.455905	+	0.0639677i
$386$	−3.24576e6			−1.10879
$387$			295703.i			0.100364i
$388$			167369.i			0.0564411i
$389$	877617.			0.294057			0.147028	−	0.989132i	$-0.453029\pi$
$389$	877617.			0.294057			0.147028	+	0.989132i	$0.453029\pi$
$390$	2.34457e6	+	328965.i	0.780551	+	0.109519i
$391$	−544210.			−0.180022
$392$		−	233151.i		−	0.0766342i
$393$			390090.i			0.127404i
$394$	1.00469e6			0.326054
$395$	−345317.	+	2.46111e6i	−0.111359	+	0.793667i
$396$	158488.			0.0507878
$397$			3.41443e6i			1.08728i	0.839318	+	0.543640i	$0.182954\pi$
$397$			3.41443e6i			1.08728i	−0.839318	+	0.543640i	$0.817046\pi$
$398$			1.25353e6i			0.396668i
$399$	3.08580e6			0.970365
$400$	−769109.	−	220161.i	−0.240347	−	0.0688002i
$401$	2.76644e6			0.859132			0.429566	−	0.903036i	$-0.358667\pi$
$401$	2.76644e6			0.859132			0.429566	+	0.903036i	$0.358667\pi$
$402$			2.23591e6i			0.690065i
$403$			4.59104e6i			1.40815i
$404$	2.00741e6			0.611904
$405$	351610.	−	2.50596e6i	0.106518	−	0.759166i
$406$	−2.11076e6			−0.635511
$407$			2.26434e6i			0.677572i
$408$			920703.i			0.273823i
$409$	4.23084e6			1.25060			0.625299	−	0.780385i	$-0.284977\pi$
$409$	4.23084e6			1.25060			0.625299	+	0.780385i	$0.284977\pi$
$410$	774187.	+	108626.i	0.227450	+	0.0319134i
$411$	1.50159e6			0.438478
$412$			2.26732e6i			0.658065i
$413$		−	607788.i		−	0.175338i
$414$	−100404.			−0.0287907
$415$	5.65445e6	+	793372.i	1.61165	+	0.226129i
$416$	−775323.			−0.219659
$417$		−	2.67461e6i		−	0.753216i
$418$			1.60600e6i			0.449577i
$419$	6.06659e6			1.68815			0.844073	−	0.536229i	$-0.180152\pi$
$419$	6.06659e6			1.68815			0.844073	+	0.536229i	$0.180152\pi$
$420$	−199398.	+	1.42113e6i	−0.0551567	+	0.393108i
$421$	1.95999e6			0.538950			0.269475	−	0.963007i	$-0.413150\pi$
$421$	1.95999e6			0.538950			0.269475	+	0.963007i	$0.413150\pi$
$422$		−	1.10287e6i		−	0.301468i
$423$			146943.i			0.0399300i
$424$	−657145.			−0.177520
$425$	884730.	−	3.09071e6i	0.237595	−	0.830016i
$426$	244506.			0.0652777
$427$			6.24535e6i			1.65763i
$428$		−	2.19182e6i		−	0.578356i
$429$	2.21030e6			0.579840
$430$	193623.	−	1.37997e6i	0.0504993	−	0.359914i
$431$	−2.76008e6			−0.715695			−0.357848	−	0.933780i	$-0.616489\pi$
$431$	−2.76008e6			−0.715695			−0.357848	+	0.933780i	$0.616489\pi$
$432$			1.03978e6i			0.268059i
$433$		−	2.10588e6i		−	0.539777i	−0.962892	−	0.269888i	$-0.913013\pi$
$433$		−	2.10588e6i		−	0.539777i	0.962892	−	0.269888i	$-0.0869868\pi$
$434$	−2.78280e6			−0.709183
$435$	−3.56045e6	−	499564.i	−0.902156	−	0.126581i
$436$	1.92965e6			0.486141
$437$		−	1.01742e6i		−	0.254857i
$438$		−	1.44119e6i		−	0.358952i
$439$	−4.63657e6			−1.14825			−0.574124	−	0.818768i	$-0.694657\pi$
$439$	−4.63657e6			−1.14825			−0.574124	+	0.818768i	$0.694657\pi$
$440$	−739625.	−	103776.i	−0.182129	−	0.0255545i
$441$	172860.			0.0423251
$442$		−	3.11568e6i		−	0.758574i
$443$			5.18509e6i			1.25530i	0.778497	+	0.627649i	$0.215983\pi$
$443$			5.18509e6i			1.25530i	−0.778497	+	0.627649i	$0.784017\pi$
$444$	−2.42689e6			−0.584242
$445$	−880188.	+	6.27320e6i	−0.210705	+	1.50172i
$446$	269752.			0.0642136
$447$			5.18369e6i			1.22707i
$448$		−	469953.i		−	0.110626i
$449$	6.46414e6			1.51319			0.756597	−	0.653882i	$-0.226861\pi$
$449$	6.46414e6			1.51319			0.756597	+	0.653882i	$0.226861\pi$
$450$	163229.	−	570223.i	0.0379984	−	0.132744i
$451$	729852.			0.168964
$452$		−	3.47928e6i		−	0.801021i
$453$		−	4.09705e6i		−	0.938049i
$454$	4.21851e6			0.960548
$455$	674769.	−	4.80915e6i	0.152801	−	1.08903i
$456$	−1.72129e6			−0.387651
$457$			6.83116e6i			1.53004i	0.644005	+	0.765022i	$0.277272\pi$
$457$			6.83116e6i			1.53004i	−0.644005	+	0.765022i	$0.722728\pi$
$458$			1.00795e6i			0.224532i
$459$	−4.17841e6			−0.925719
$460$	468562.	+	65743.6i	0.103246	+	0.0144864i
$461$	−2.15573e6			−0.472436			−0.236218	−	0.971700i	$-0.575908\pi$
$461$	−2.15573e6			−0.472436			−0.236218	+	0.971700i	$0.575908\pi$
$462$			1.33975e6i			0.292024i
$463$			4.45364e6i			0.965523i	0.875752	+	0.482762i	$0.160366\pi$
$463$			4.45364e6i			0.965523i	−0.875752	+	0.482762i	$0.839634\pi$
$464$	1.17740e6			0.253880
$465$	−4.69406e6	−	658621.i	−1.00674	−	0.141255i
$466$	−1.09209e6			−0.232966
$467$			1.95904e6i			0.415672i	0.978164	+	0.207836i	$0.0666421\pi$
$467$			1.95904e6i			0.415672i	−0.978164	+	0.207836i	$0.933358\pi$
$468$		−	574830.i		−	0.121318i
$469$	4.58628e6			0.962783
$470$	96216.8	−	685748.i	0.0200912	−	0.143192i
$471$	−5.31789e6			−1.10455
$472$			339030.i			0.0700459i
$473$		−	1.30094e6i		−	0.267366i
$474$	−2.48673e6			−0.508373
$475$	5.77820e6	+	1.65403e6i	1.17506	+	0.336365i
$476$	1.88853e6			0.382039
$477$		−	487212.i		−	0.0980443i
$478$		−	2.31588e6i		−	0.463604i
$479$	−404518.			−0.0805562			−0.0402781	−	0.999189i	$-0.512824\pi$
$479$	−404518.			−0.0805562			−0.0402781	+	0.999189i	$0.512824\pi$
$480$	111226.	−	792721.i	0.0220345	−	0.157043i
$481$	8.21266e6			1.61853
$482$		−	2.41074e6i		−	0.472642i
$483$		−	848748.i		−	0.165543i
$484$	1.87955e6			0.364703
$485$	579091.	+	81251.9i	0.111787	+	0.0156848i
$486$	−1.41586e6			−0.271912
$487$			8.12511e6i			1.55241i	0.630479	+	0.776206i	$0.282858\pi$
$487$			8.12511e6i			1.55241i	−0.630479	+	0.776206i	$0.717142\pi$
$488$		−	3.48371e6i		−	0.662206i
$489$	−7.21307e6			−1.36411
$490$	−806695.	−	113187.i	−0.151782	−	0.0212964i
$491$	−5.42700e6			−1.01591			−0.507956	−	0.861383i	$-0.669599\pi$
$491$	−5.42700e6			−1.01591			−0.507956	+	0.861383i	$0.669599\pi$
$492$			782246.i			0.145690i
$493$			4.73146e6i			0.876754i
$494$	5.82488e6			1.07391
$495$	76940.5	−	548364.i	0.0141137	−	0.100590i
$496$	1.55227e6			0.283311
$497$		−	501527.i		−	0.0910758i
$498$			5.71331e6i			1.03232i
$499$	−9.58639e6			−1.72347			−0.861735	−	0.507358i	$-0.830622\pi$
$499$	−9.58639e6			−1.72347			−0.861735	+	0.507358i	$0.830622\pi$
$500$	−1.13512e6	+	2.55421e6i	−0.203057	+	0.456911i
$501$	−5.26255e6			−0.936704
$502$		−	1.63084e6i		−	0.288837i
$503$			1.07252e7i			1.89011i	0.326913	+	0.945054i	$0.393992\pi$
$503$			1.07252e7i			1.89011i	−0.326913	+	0.945054i	$0.606008\pi$
$504$	348426.			0.0610991
$505$	974529.	−	6.94557e6i	0.170046	−	1.21194i
$506$	441729.			0.0766972
$507$		−	2.82454e6i		−	0.488009i
$508$		−	2.42967e6i		−	0.417722i
$509$	2.04903e6			0.350553			0.175277	−	0.984519i	$-0.443918\pi$
$509$	2.04903e6			0.350553			0.175277	+	0.984519i	$0.443918\pi$
$510$	3.18560e6	+	446969.i	0.542333	+	0.0760943i
$511$	−2.95616e6			−0.500813
$512$			262144.i			0.0441942i
$513$		−	7.81169e6i		−	1.31054i
$514$	−469454.			−0.0783764
$515$	7.84483e6	+	1.10070e6i	1.30336	+	0.182874i
$516$	1.39434e6			0.230538
$517$		−	646477.i		−	0.106372i
$518$			4.97801e6i			0.815138i
$519$	−289314.			−0.0471467
$520$	−376392.	+	2.68259e6i	−0.0610425	+	0.435057i
$521$	1.19223e7			1.92427			0.962137	−	0.272567i	$-0.0878725\pi$
$521$	1.19223e7			1.92427			0.962137	+	0.272567i	$0.0878725\pi$
$522$			872933.i			0.140218i
$523$		−	1.01600e7i		−	1.62420i	−0.583519	−	0.812099i	$-0.698325\pi$
$523$		−	1.01600e7i		−	1.62420i	0.583519	−	0.812099i	$-0.301675\pi$
$524$	−446330.			−0.0710114
$525$	4.82027e6	+	1.37982e6i	0.763261	+	0.218486i
$526$	3.74845e6			0.590727
$527$			6.23791e6i			0.978391i
$528$		−	747324.i		−	0.116661i
$529$	−279841.			−0.0434783
$530$	−319021.	+	2.27370e6i	−0.0493321	+	0.351596i
$531$	−251359.			−0.0386864
$532$			3.53068e6i			0.540853i
$533$		−	2.64714e6i		−	0.403607i
$534$	−6.33850e6			−0.961907
$535$	−7.58361e6	−	1.06405e6i	−1.14549	−	0.160723i
$536$	−2.55827e6			−0.384622
$537$			4.67862e6i			0.700135i
$538$			6.47951e6i			0.965131i
$539$	−760498.			−0.112752
$540$	3.59759e6	+	504776.i	0.530918	+	0.0744928i
$541$	−8.64940e6			−1.27055			−0.635276	−	0.772285i	$-0.719114\pi$
$541$	−8.64940e6			−1.27055			−0.635276	+	0.772285i	$0.719114\pi$
$542$		−	5.15797e6i		−	0.754190i
$543$		−	1.01393e7i		−	1.47573i
$544$	−1.05344e6			−0.152621
$545$	936778.	−	6.67652e6i	0.135097	−	0.962851i
$546$	4.85921e6			0.697564
$547$			5.60937e6i			0.801578i	0.916170	+	0.400789i	$0.131264\pi$
$547$			5.60937e6i			0.801578i	−0.916170	+	0.400789i	$0.868736\pi$
$548$			1.71808e6i			0.244395i
$549$	2.58285e6			0.365737
$550$	−718125.	+	2.50870e6i	−0.101226	+	0.353624i
$551$	−8.84563e6			−1.24122
$552$			473439.i			0.0661328i
$553$			5.10074e6i			0.709285i
$554$	2.52815e6			0.349968
$555$	−1.17817e6	+	8.39695e6i	−0.162359	+	1.15715i
$556$	3.06021e6			0.419821
$557$		−	1.26142e7i		−	1.72275i	−0.507971	−	0.861374i	$-0.669604\pi$
$557$		−	1.26142e7i		−	1.72275i	0.507971	−	0.861374i	$-0.330396\pi$
$558$			1.15087e6i			0.156473i
$559$	−4.71847e6			−0.638663
$560$	−1.62602e6	−	228146.i	−0.219107	−	0.0307427i
$561$	3.00317e6			0.402877
$562$			1.67149e6i			0.223236i
$563$		−	8.23445e6i		−	1.09487i	−0.836847	−	0.547437i	$-0.815604\pi$
$563$		−	8.23445e6i		−	1.09487i	0.836847	−	0.547437i	$-0.184396\pi$
$564$	692886.			0.0917200
$565$	−1.20382e7	−	1.68907e6i	−1.58650	−	0.222601i
$566$	337429.			0.0442733
$567$		−	5.19370e6i		−	0.678452i
$568$			279756.i			0.0363839i
$569$	−1.32336e7			−1.71355			−0.856773	−	0.515693i	$-0.827535\pi$
$569$	−1.32336e7			−1.71355			−0.856773	+	0.515693i	$0.827535\pi$
$570$	−835625.	+	5.95559e6i	−0.107727	+	0.767782i
$571$	−6.53831e6			−0.839219			−0.419609	−	0.907705i	$-0.637833\pi$
$571$	−6.53831e6			−0.839219			−0.419609	+	0.907705i	$0.637833\pi$
$572$			2.52896e6i			0.323186i
$573$		−	6.20212e6i		−	0.789140i
$574$	1.60453e6			0.203268
$575$	454941.	−	1.58929e6i	0.0573833	−	0.200463i
$576$	−194355.			−0.0244085
$577$			3.66228e6i			0.457944i	0.973433	+	0.228972i	$0.0735364\pi$
$577$			3.66228e6i			0.457944i	−0.973433	+	0.228972i	$0.926464\pi$
$578$			1.44610e6i			0.180045i
$579$	−1.13471e7			−1.40666
$580$	571587.	−	4.07376e6i	0.0705525	−	0.502835i
$581$	1.17191e7			1.44030
$582$			585119.i			0.0716039i
$583$			2.14349e6i			0.261186i
$584$	1.64897e6			0.200070
$585$	−1.98889e6	−	279060.i	−0.240282	−	0.0337138i
$586$	−4.63464e6			−0.557535
$587$		−	1.16820e6i		−	0.139933i	−0.997549	−	0.0699667i	$-0.977711\pi$
$587$		−	1.16820e6i		−	0.139933i	0.997549	−	0.0699667i	$-0.0222893\pi$
$588$		−	815092.i		−	0.0972217i
$589$	−1.16620e7			−1.38511
$590$	1.17303e6	+	164587.i	0.138733	+	0.0194655i
$591$	3.51236e6			0.413648
$592$		−	2.77678e6i		−	0.325639i
$593$		−	6.84373e6i		−	0.799201i	−0.916689	−	0.399601i	$-0.869149\pi$
$593$		−	6.84373e6i		−	0.799201i	0.916689	−	0.399601i	$-0.130851\pi$
$594$	3.39157e6			0.394398
$595$	916818.	−	6.53426e6i	0.106167	−	0.756666i
$596$	−5.93103e6			−0.683934
$597$			4.38232e6i			0.503232i
$598$		−	1.60213e6i		−	0.183208i
$599$	1.77214e6			0.201804			0.100902	−	0.994896i	$-0.467827\pi$
$599$	1.77214e6			0.201804			0.100902	+	0.994896i	$0.467827\pi$
$600$	−2.68879e6	−	769677.i	−0.304915	−	0.0872832i
$601$	−7.18815e6			−0.811766			−0.405883	−	0.913925i	$-0.633036\pi$
$601$	−7.18815e6			−0.811766			−0.405883	+	0.913925i	$0.633036\pi$
$602$		−	2.86004e6i		−	0.321649i
$603$		−	1.89672e6i		−	0.212427i
$604$	4.68772e6			0.522841
$605$	912455.	−	6.50317e6i	0.101350	−	0.722331i
$606$	7.01787e6			0.776290
$607$			2.47513e6i			0.272663i	0.990663	+	0.136332i	$0.0435312\pi$
$607$			2.47513e6i			0.272663i	−0.990663	+	0.136332i	$0.956469\pi$
$608$		−	1.96945e6i		−	0.216066i
$609$	−7.37916e6			−0.806239
$610$	−1.20535e7	−	1.69122e6i	−1.31156	−	0.184025i
$611$	−2.34474e6			−0.254093
$612$		−	781030.i		−	0.0842925i
$613$			594699.i			0.0639213i	0.999489	+	0.0319607i	$0.0101751\pi$
$613$			594699.i			0.0639213i	−0.999489	+	0.0319607i	$0.989825\pi$
$614$	1.13344e7			1.21333
$615$	2.70654e6	+	379753.i	0.288554	+	0.0404868i
$616$	−1.53290e6			−0.162766
$617$		−	4.38364e6i		−	0.463577i	−0.972766	−	0.231788i	$-0.925542\pi$
$617$		−	4.38364e6i		−	0.463577i	0.972766	−	0.231788i	$-0.0744577\pi$
$618$			7.92649e6i			0.834852i
$619$	1.12773e7			1.18298			0.591491	−	0.806311i	$-0.298539\pi$
$619$	1.12773e7			1.18298			0.591491	+	0.806311i	$0.298539\pi$
$620$	753575.	−	5.37081e6i	0.0787313	−	0.561126i
$621$	−2.14860e6			−0.223577
$622$			2.03438e6i			0.210842i
$623$			1.30014e7i			1.34206i
$624$	−2.71051e6			−0.278670
$625$	8.28642e6	+	5.16747e6i	0.848529	+	0.529149i
$626$	4.31890e6			0.440491
$627$			5.61453e6i			0.570354i
$628$		−	6.08457e6i		−	0.615646i
$629$	1.11587e7			1.12457
$630$	169149.	−	1.20554e6i	0.0169792	−	0.121013i
$631$	−1.27384e6			−0.127363			−0.0636813	−	0.997970i	$-0.520284\pi$
$631$	−1.27384e6			−0.127363			−0.0636813	+	0.997970i	$0.520284\pi$
$632$		−	2.84524e6i		−	0.283352i
$633$		−	3.85560e6i		−	0.382457i
$634$	1.27005e7			1.25487
$635$	−8.40656e6	−	1.17952e6i	−0.827340	−	0.116083i
$636$	−2.29737e6			−0.225210
$637$			2.75829e6i			0.269334i
$638$		−	3.84047e6i		−	0.373536i
$639$	−207413.			−0.0200948
$640$	907009.	+	127262.i	0.0875309	+	0.0122814i
$641$	7.84981e6			0.754595			0.377298	−	0.926092i	$-0.376853\pi$
$641$	7.84981e6			0.754595			0.377298	+	0.926092i	$0.376853\pi$
$642$		−	7.66255e6i		−	0.733729i
$643$		−	1.43864e7i		−	1.37222i	−0.727497	−	0.686111i	$-0.759317\pi$
$643$		−	1.43864e7i		−	1.37222i	0.727497	−	0.686111i	$-0.240683\pi$
$644$	971113.			0.0922689
$645$	676902.	−	4.82435e6i	0.0640658	−	0.456604i
$646$	7.91435e6			0.746163
$647$		−	2.16317e6i		−	0.203156i	−0.994828	−	0.101578i	$-0.967611\pi$
$647$		−	2.16317e6i		−	0.203156i	0.994828	−	0.101578i	$-0.0323892\pi$
$648$			2.89710e6i			0.271035i
$649$	1.10585e6			0.103059
$650$	9.09894e6	+	2.60461e6i	0.844709	+	0.241801i
$651$	−9.72862e6			−0.899702
$652$		−	8.25299e6i		−	0.760312i
$653$		−	2.25198e6i		−	0.206672i	−0.994646	−	0.103336i	$-0.967048\pi$
$653$		−	2.25198e6i		−	0.206672i	0.994646	−	0.103336i	$-0.0329518\pi$
$654$	6.74602e6			0.616742
$655$	−216678.	+	1.54429e6i	−0.0197338	+	0.140645i
$656$	−895024.			−0.0812035
$657$			1.22256e6i			0.110499i
$658$		−	1.42124e6i		−	0.127968i
$659$	−1.08353e7			−0.971916			−0.485958	−	0.873982i	$-0.661529\pi$
$659$	−1.08353e7			−0.971916			−0.485958	+	0.873982i	$0.661529\pi$
$660$	−2.58571e6	−	362800.i	−0.231058	−	0.0324196i
$661$	1.48392e7			1.32102			0.660508	−	0.750819i	$-0.270341\pi$
$661$	1.48392e7			1.32102			0.660508	+	0.750819i	$0.270341\pi$
$662$		−	1.31692e7i		−	1.16793i
$663$		−	1.08924e7i		−	0.962362i
$664$	−6.53700e6			−0.575385
$665$	1.22160e7	+	1.71402e6i	1.07121	+	0.150301i
$666$	2.05872e6			0.179851
$667$			2.43299e6i			0.211751i
$668$		−	6.02126e6i		−	0.522091i
$669$	943047.			0.0814644
$670$	−1.24195e6	+	8.85152e6i	−0.106885	+	0.761783i
$671$	−1.13633e7			−0.974308
$672$		−	1.64294e6i		−	0.140346i
$673$			1.95395e7i			1.66294i	0.555570	+	0.831470i	$0.312500\pi$
$673$			1.95395e7i			1.66294i	−0.555570	+	0.831470i	$0.687500\pi$
$674$	−1.37806e7			−1.16847
$675$	3.49301e6	−	1.22025e7i	0.295081	−	1.03083i
$676$	3.23176e6			0.272002
$677$			8.13422e6i			0.682094i	0.940046	+	0.341047i	$0.110782\pi$
$677$			8.13422e6i			0.682094i	−0.940046	+	0.341047i	$0.889218\pi$
$678$		−	1.21635e7i		−	1.01621i
$679$	1.20019e6			0.0999021
$680$	−511410.	+	3.64487e6i	−0.0424128	+	0.302280i
$681$	1.47478e7			1.21860
$682$		−	5.06324e6i		−	0.416838i
$683$		−	1.33434e7i		−	1.09450i	−0.836971	−	0.547248i	$-0.815676\pi$
$683$		−	1.33434e7i		−	1.09450i	0.836971	−	0.547248i	$-0.184324\pi$
$684$	1.46016e6			0.119333
$685$	5.94450e6	+	834069.i	0.484048	+	0.0679165i
$686$	−9.38528e6			−0.761442
$687$			3.52379e6i			0.284851i
$688$			1.59536e6i			0.128495i
$689$	7.77435e6			0.623902
$690$	1.63808e6	+	229838.i	0.130983	+	0.0183781i
$691$	−5.63941e6			−0.449303			−0.224651	−	0.974439i	$-0.572124\pi$
$691$	−5.63941e6			−0.449303			−0.224651	+	0.974439i	$0.572124\pi$
$692$		−	331025.i		−	0.0262782i
$693$		−	1.13650e6i		−	0.0898955i
$694$	5.04745e6			0.397808
$695$	1.48563e6	−	1.05882e7i	0.116667	−	0.831497i
$696$	4.11617e6			0.322085
$697$		−	3.59671e6i		−	0.280429i
$698$			1.03875e7i			0.807001i
$699$	−3.81792e6			−0.295552
$700$	−1.57875e6	+	5.51521e6i	−0.121778	+	0.425419i
$701$	1.68717e6			0.129677			0.0648386	−	0.997896i	$-0.479347\pi$
$701$	1.68717e6			0.129677			0.0648386	+	0.997896i	$0.479347\pi$
$702$		−	1.23011e7i		−	0.942107i
$703$			2.08615e7i			1.59205i
$704$	855067.			0.0650232
$705$	336372.	−	2.39736e6i	0.0254887	−	0.181661i
$706$	4.98142e6			0.376133
$707$		−	1.43950e7i		−	1.08308i
$708$			1.18524e6i			0.0888635i
$709$	−3.21870e6			−0.240472			−0.120236	−	0.992745i	$-0.538365\pi$
$709$	−3.21870e6			−0.240472			−0.120236	+	0.992745i	$0.538365\pi$
$710$	967947.	+	135812.i	0.0720619	+	0.0101110i
$711$	2.10948e6			0.156496
$712$		−	7.25233e6i		−	0.536139i
$713$			3.20763e6i			0.236298i
$714$	6.60228e6			0.484672
$715$	8.75013e6	+	1.22772e6i	0.640102	+	0.0898123i
$716$	−5.35314e6			−0.390235
$717$		−	8.09628e6i		−	0.588150i
$718$		−	1.05126e6i		−	0.0761025i
$719$	−8.01355e6			−0.578099			−0.289050	−	0.957314i	$-0.593339\pi$
$719$	−8.01355e6			−0.578099			−0.289050	+	0.957314i	$0.593339\pi$
$720$	−94352.8	+	672463.i	−0.00678303	+	0.0483434i
$721$	1.62587e7			1.16479
$722$			4.89176e6i			0.349238i
$723$		−	8.42789e6i		−	0.599616i
$724$	1.16011e7			0.822529
$725$	−1.38176e7	−	3.95534e6i	−0.976309	−	0.279472i
$726$	6.57086e6			0.462680
$727$		−	8.09033e6i		−	0.567715i	−0.958867	−	0.283857i	$-0.908386\pi$
$727$		−	8.09033e6i		−	0.567715i	0.958867	−	0.283857i	$-0.0916142\pi$
$728$			5.55977e6i			0.388802i
$729$	−1.59497e7			−1.11156
$730$	800519.	−	5.70539e6i	0.0555987	−	0.396258i
$731$	−6.41105e6			−0.443748
$732$		−	1.21790e7i		−	0.840105i
$733$			1.77542e7i			1.22051i	0.792205	+	0.610254i	$0.208933\pi$
$733$			1.77542e7i			1.22051i	−0.792205	+	0.610254i	$0.791067\pi$
$734$	−1.60418e7			−1.09904
$735$	−2.82019e6	−	395699.i	−0.192557	−	0.0270176i
$736$	−541696.			−0.0368605
$737$			8.34462e6i			0.565898i
$738$		−	663577.i		−	0.0448488i
$739$	6.92864e6			0.466699			0.233349	−	0.972393i	$-0.425031\pi$
$739$	6.92864e6			0.466699			0.233349	+	0.972393i	$0.425031\pi$
$740$	−9.60755e6	−	1.34803e6i	−0.644961	−	0.0904941i
$741$	2.03637e7			1.36242
$742$			4.71233e6i			0.314214i
$743$			2.84559e7i			1.89104i	0.325571	+	0.945518i	$0.394444\pi$
$743$			2.84559e7i			1.89104i	−0.325571	+	0.945518i	$0.605556\pi$
$744$	5.42672e6			0.359422
$745$	−2.87931e6	+	2.05211e7i	−0.190063	+	1.35460i
$746$	5.17264e6			0.340303
$747$		−	4.84658e6i		−	0.317786i
$748$			3.43614e6i			0.224552i
$749$	−1.57173e7			−1.02370
$750$	−3.96837e6	+	8.92947e6i	−0.257608	+	0.579659i
$751$	2.32342e7			1.50324			0.751618	−	0.659599i	$-0.229274\pi$
$751$	2.32342e7			1.50324			0.751618	+	0.659599i	$0.229274\pi$
$752$			792780.i			0.0511221i
$753$		−	5.70138e6i		−	0.366432i
$754$	−1.39292e7			−0.892274
$755$	2.27573e6	−	1.62194e7i	0.145296	−	1.03554i
$756$	7.45615e6			0.474471
$757$		−	1.15860e7i		−	0.734843i	−0.930054	−	0.367422i	$-0.880241\pi$
$757$		−	1.15860e7i		−	0.734843i	0.930054	−	0.367422i	$-0.119759\pi$
$758$		−	1.06533e6i		−	0.0673458i
$759$	1.54428e6			0.0973017
$760$	−6.81422e6	−	956098.i	−0.427939	−	0.0600439i
$761$	−1.77781e7			−1.11282			−0.556409	−	0.830909i	$-0.687821\pi$
$761$	−1.77781e7			−1.11282			−0.556409	+	0.830909i	$0.687821\pi$
$762$		−	8.49406e6i		−	0.529942i
$763$		−	1.38373e7i		−	0.860482i
$764$	7.09629e6			0.439844
$765$	−2.70234e6	−	379163.i	−0.166950	−	0.0234246i
$766$	1.48358e7			0.913567
$767$		−	4.01089e6i		−	0.246180i
$768$			916450.i			0.0560668i
$769$	1.45352e7			0.886348			0.443174	−	0.896436i	$-0.353852\pi$
$769$	1.45352e7			0.886348			0.443174	+	0.896436i	$0.353852\pi$
$770$	−744171.	+	5.30379e6i	−0.0452320	+	0.322373i
$771$	−1.64120e6			−0.0994320
$772$		−	1.29830e7i		−	0.784031i
$773$			1.18159e7i			0.711244i	0.934630	+	0.355622i	$0.115731\pi$
$773$			1.18159e7i			0.711244i	−0.934630	+	0.355622i	$0.884269\pi$
$774$	−1.18281e6			−0.0709681
$775$	−1.82170e7	−	5.21469e6i	−1.08949	−	0.311870i
$776$	−669476.			−0.0399099
$777$			1.74030e7i			1.03412i
$778$			3.51047e6i			0.207930i
$779$	6.72417e6			0.397004
$780$	−1.31586e6	+	9.37828e6i	−0.0774414	+	0.551933i
$781$	912515.			0.0535319
$782$		−	2.17684e6i		−	0.127294i
$783$			1.86803e7i			1.08888i
$784$	932605.			0.0541885
$785$	−2.10524e7	−	2.95385e6i	−1.21935	−	0.171086i
$786$	−1.56036e6			−0.0900884
$787$		−	1.62523e7i		−	0.935360i	−0.883898	−	0.467680i	$-0.845090\pi$
$787$		−	1.62523e7i		−	0.935360i	0.883898	−	0.467680i	$-0.154910\pi$
$788$			4.01875e6i			0.230555i
$789$	1.31045e7			0.749424
$790$	−9.84444e6	−	1.38127e6i	−0.561207	−	0.0787426i
$791$	−2.49496e7			−1.41783
$792$			633953.i			0.0359124i
$793$			4.12140e7i			2.32735i
$794$	−1.36577e7			−0.768823
$795$	−1.11529e6	+	7.94881e6i	−0.0625851	+	0.446051i
$796$	−5.01412e6			−0.280487
$797$			4.69382e6i			0.261747i	0.991399	+	0.130873i	$0.0417781\pi$
$797$			4.69382e6i			0.261747i	−0.991399	+	0.130873i	$0.958222\pi$
$798$			1.23432e7i			0.686152i
$799$	−3.18584e6			−0.176546
$800$	880643.	−	3.07644e6i	0.0486491	−	0.169951i
$801$	5.37693e6			0.296110
$802$			1.10657e7i			0.607498i
$803$		−	5.37865e6i		−	0.294364i
$804$	−8.94366e6			−0.487950
$805$	471442.	−	3.36002e6i	0.0256412	−	0.182748i
$806$	−1.83642e7			−0.995711
$807$			2.26522e7i			1.22441i
$808$			8.02965e6i			0.432681i
$809$	6.85605e6			0.368301			0.184150	−	0.982898i	$-0.441047\pi$
$809$	6.85605e6			0.368301			0.184150	+	0.982898i	$0.441047\pi$
$810$	1.00238e7	+	1.40644e6i	0.536812	+	0.0753197i
$811$	−2.13768e6			−0.114128			−0.0570639	−	0.998371i	$-0.518174\pi$
$811$	−2.13768e6			−0.114128			−0.0570639	+	0.998371i	$0.518174\pi$
$812$		−	8.44303e6i		−	0.449374i
$813$		−	1.80322e7i		−	0.956801i
$814$	−9.05736e6			−0.479116
$815$	−2.85550e7	−	4.00654e6i	−1.50587	−	0.211288i
$816$	−3.68281e6			−0.193622
$817$		−	1.19857e7i		−	0.628215i
$818$			1.69233e7i			0.884307i
$819$	−4.12205e6			−0.214735
$820$	−434503.	+	3.09675e6i	−0.0225662	+	0.160832i
$821$	−764211.			−0.0395691			−0.0197845	−	0.999804i	$-0.506298\pi$
$821$	−764211.			−0.0395691			−0.0197845	+	0.999804i	$0.506298\pi$
$822$			6.00638e6i			0.310051i
$823$			1.33243e7i			0.685718i	0.939387	+	0.342859i	$0.111395\pi$
$823$			1.33243e7i			0.685718i	−0.939387	+	0.342859i	$0.888605\pi$
$824$	−9.06926e6			−0.465322
$825$	−2.51055e6	+	8.77036e6i	−0.128420	+	0.448624i
$826$	2.43115e6			0.123983
$827$		−	1.00663e7i		−	0.511809i	−0.966702	−	0.255905i	$-0.917627\pi$
$827$		−	1.00663e7i		−	0.511809i	0.966702	−	0.255905i	$-0.0823733\pi$
$828$		−	401617.i		−	0.0203581i
$829$	1.91526e7			0.967925			0.483962	−	0.875089i	$-0.339197\pi$
$829$	1.91526e7			0.967925			0.483962	+	0.875089i	$0.339197\pi$
$830$	−3.17349e6	+	2.26178e7i	−0.159898	+	1.13961i
$831$	8.83835e6			0.443985
$832$		−	3.10129e6i		−	0.155322i
$833$			3.74773e6i			0.187135i
$834$	1.06984e7			0.532604
$835$	−2.08334e7	−	2.92311e6i	−1.03405	−	0.145087i
$836$	−6.42399e6			−0.317899
$837$			2.46280e7i			1.21511i
$838$			2.42664e7i			1.19370i
$839$	7.19059e6			0.352663			0.176331	−	0.984331i	$-0.443577\pi$
$839$	7.19059e6			0.352663			0.176331	+	0.984331i	$0.443577\pi$
$840$	−5.68453e6	−	797593.i	−0.277969	−	0.0390016i
$841$	641669.			0.0312839
$842$			7.83995e6i			0.381095i
$843$			5.84350e6i			0.283207i
$844$	4.41147e6			0.213170
$845$	1.56891e6	−	1.11818e7i	0.0755884	−	0.538727i
$846$	−587773.			−0.0282347
$847$		−	1.34781e7i		−	0.645534i
$848$		−	2.62858e6i		−	0.125525i
$849$	1.17965e6			0.0561672
$850$	1.23629e7	+	3.53892e6i	0.586910	+	0.168005i
$851$	5.73795e6			0.271602
$852$			978022.i			0.0461583i
$853$		−	9.62714e6i		−	0.453028i	−0.974008	−	0.226514i	$-0.927267\pi$
$853$		−	9.62714e6i		−	0.453028i	0.974008	−	0.226514i	$-0.0727329\pi$
$854$	−2.49814e7			−1.17212
$855$	708858.	−	5.05211e6i	0.0331623	−	0.236351i
$856$	8.76727e6			0.408959
$857$			1.48353e7i			0.689992i	0.938604	+	0.344996i	$0.112120\pi$
$857$			1.48353e7i			0.689992i	−0.938604	+	0.344996i	$0.887880\pi$
$858$			8.84121e6i			0.410009i
$859$	7.72123e6			0.357029			0.178515	−	0.983937i	$-0.442871\pi$
$859$	7.72123e6			0.357029			0.178515	+	0.983937i	$0.442871\pi$
$860$	5.51989e6	+	774492.i	0.254498	+	0.0357084i
$861$	5.60941e6			0.257875
$862$		−	1.10403e7i		−	0.506073i
$863$		−	2.57381e7i		−	1.17639i	−0.808721	−	0.588193i	$-0.799840\pi$
$863$		−	2.57381e7i		−	1.17639i	0.808721	−	0.588193i	$-0.200160\pi$
$864$	−4.15911e6			−0.189547
$865$	−1.14534e6	−	160701.i	−0.0520466	−	0.00730263i
$866$	8.42353e6			0.381680
$867$			5.05555e6i			0.228413i
$868$		−	1.11312e7i		−	0.501468i
$869$	−9.28068e6			−0.416898
$870$	1.99826e6	−	1.42418e7i	0.0895062	−	0.637920i
$871$	3.02656e7			1.35177
$872$			7.71860e6i			0.343754i
$873$		−	496355.i		−	0.0220423i
$874$	4.06968e6			0.180211
$875$	1.83160e7	+	8.13987e6i	0.808743	+	0.359416i
$876$	5.76477e6			0.253818
$877$			3.95324e7i			1.73562i	0.496896	+	0.867810i	$0.334473\pi$
$877$			3.95324e7i			1.73562i	−0.496896	+	0.867810i	$0.665527\pi$
$878$		−	1.85463e7i		−	0.811934i
$879$	−1.62026e7			−0.707315
$880$	415105.	−	2.95850e6i	0.0180697	−	0.128785i
$881$	2.29721e7			0.997151			0.498576	−	0.866846i	$-0.333857\pi$
$881$	2.29721e7			0.997151			0.498576	+	0.866846i	$0.333857\pi$
$882$			691440.i			0.0299284i
$883$			486213.i			0.0209858i	0.999945	+	0.0104929i	$0.00334005\pi$
$883$			486213.i			0.0209858i	−0.999945	+	0.0104929i	$0.996660\pi$
$884$	1.24627e7			0.536392
$885$	4.10089e6	+	575393.i	0.176003	+	0.0246949i
$886$	−2.07403e7			−0.887629
$887$			3.32439e7i			1.41874i	0.704837	+	0.709369i	$0.251020\pi$
$887$			3.32439e7i			1.41874i	−0.704837	+	0.709369i	$0.748980\pi$
$888$		−	9.70756e6i		−	0.413121i
$889$	−1.74229e7			−0.739378
$890$	−2.50928e7	−	3.52075e6i	−1.06188	−	0.148991i
$891$	9.44981e6			0.398776
$892$			1.07901e6i			0.0454059i
$893$		−	5.95604e6i		−	0.249936i
$894$	−2.07347e7			−0.867670
$895$	−2.59876e6	+	1.85217e7i	−0.108445	+	0.772899i
$896$	1.87981e6			0.0782247
$897$		−	5.60102e6i		−	0.232427i
$898$			2.58565e7i			1.06999i
$899$	2.78877e7			1.15084
$900$	2.28089e6	+	652915.i	0.0938639	+	0.0268689i
$901$	1.05631e7			0.433491
$902$			2.91941e6i			0.119475i
$903$		−	9.99866e6i		−	0.408058i
$904$	1.39171e7			0.566407
$905$	5.63191e6	−	4.01392e7i	0.228578	−	1.62910i
$906$	1.63882e7			0.663301
$907$			2.44256e6i			0.0985888i	0.998784	+	0.0492944i	$0.0156973\pi$
$907$			2.44256e6i			0.0985888i	−0.998784	+	0.0492944i	$0.984303\pi$
$908$			1.68740e7i			0.679210i
$909$	−5.95324e6			−0.238970
$910$	1.92366e7	+	2.69907e6i	0.770061	+	0.108047i
$911$	−9.25256e6			−0.369374			−0.184687	−	0.982797i	$-0.559127\pi$
$911$	−9.25256e6			−0.369374			−0.184687	+	0.982797i	$0.559127\pi$
$912$		−	6.88515e6i		−	0.274111i
$913$			2.13225e7i			0.846568i
$914$	−2.73246e7			−1.08190
$915$	−4.21389e7	−	5.91248e6i	−1.66391	−	0.233462i
$916$	−4.03182e6			−0.158768
$917$			3.20059e6i			0.125692i
$918$		−	1.67136e7i		−	0.654582i
$919$	−7.49713e6			−0.292824			−0.146412	−	0.989224i	$-0.546772\pi$
$919$	−7.49713e6			−0.292824			−0.146412	+	0.989224i	$0.546772\pi$
$920$	−262975.	+	1.87425e6i	−0.0102434	+	0.0730059i
$921$	3.96249e7			1.53928
$922$		−	8.62293e6i		−	0.334063i
$923$		−	3.30965e6i		−	0.127873i
$924$	−5.35899e6			−0.206492
$925$	−9.32827e6	+	3.25874e7i	−0.358465	+	1.25226i
$926$	−1.78146e7			−0.682728
$927$		−	6.72402e6i		−	0.256998i
$928$			4.70960e6i			0.179521i
$929$	3.10194e7			1.17922			0.589609	−	0.807689i	$-0.299282\pi$
$929$	3.10194e7			1.17922			0.589609	+	0.807689i	$0.299282\pi$
$930$	2.63448e6	−	1.87762e7i	0.0998822	−	0.711871i
$931$	−7.00652e6			−0.264928
$932$		−	4.36836e6i		−	0.164732i
$933$			7.11215e6i			0.267483i
$934$	−7.83616e6			−0.293925
$935$	1.18889e7	+	1.66813e6i	0.444748	+	0.0624022i
$936$	2.29932e6			0.0857847
$937$			3.97391e7i			1.47866i	0.673342	+	0.739331i	$0.264858\pi$
$937$			3.97391e7i			1.47866i	−0.673342	+	0.739331i	$0.735142\pi$
$938$			1.83451e7i			0.680791i
$939$	1.50988e7			0.558828
$940$	2.74299e6	+	384867.i	0.101252	+	0.0142066i
$941$	5.02153e7			1.84868			0.924341	−	0.381566i	$-0.124615\pi$
$941$	5.02153e7			1.84868			0.924341	+	0.381566i	$0.124615\pi$
$942$		−	2.12715e7i		−	0.781037i
$943$		−	1.84948e6i		−	0.0677284i
$944$	−1.35612e6			−0.0495300
$945$	3.61970e6	−	2.57980e7i	0.131854	−	0.939738i
$946$	5.20378e6			0.189056
$947$		−	1.61914e7i		−	0.586690i	−0.956007	−	0.293345i	$-0.905232\pi$
$947$		−	1.61914e7i		−	0.586690i	0.956007	−	0.293345i	$-0.0947685\pi$
$948$		−	9.94691e6i		−	0.359474i
$949$	−1.95081e7			−0.703154
$950$	−6.61613e6	+	2.31128e7i	−0.237846	+	0.830890i
$951$	4.44008e7			1.59199
$952$			7.55414e6i			0.270142i
$953$		−	4.63598e7i		−	1.65352i	−0.562556	−	0.826759i	$-0.690182\pi$
$953$		−	4.63598e7i		−	1.65352i	0.562556	−	0.826759i	$-0.309818\pi$
$954$	1.94885e6			0.0693278
$955$	3.44500e6	−	2.45529e7i	0.122231	−	0.871154i
$956$	9.26354e6			0.327817
$957$		−	1.34262e7i		−	0.473885i
$958$		−	1.61807e6i		−	0.0569618i
$959$	1.23202e7			0.432585
$960$	3.17088e6	+	444905.i	0.111046	+	0.0155808i
$961$	8.13772e6			0.284246
$962$			3.28506e7i			1.14447i
$963$			6.50012e6i			0.225868i
$964$	9.64295e6			0.334208
$965$	−4.49209e7	−	6.30282e6i	−1.55285	−	0.217880i
$966$	3.39499e6			0.117057
$967$			6.39991e6i			0.220094i	0.993926	+	0.110047i	$0.0351001\pi$
$967$			6.39991e6i			0.220094i	−0.993926	+	0.110047i	$0.964900\pi$
$968$			7.51819e6i			0.257884i
$969$	2.76684e7			0.946618
$970$	−325007.	+	2.31636e6i	−0.0110908	+	0.0790455i
$971$	1.98936e7			0.677120			0.338560	−	0.940945i	$-0.390060\pi$
$971$	1.98936e7			0.677120			0.338560	+	0.940945i	$0.390060\pi$
$972$		−	5.66343e6i		−	0.192271i
$973$		−	2.19445e7i		−	0.743093i
$974$	−3.25005e7			−1.09772
$975$	3.18097e7	+	9.10566e6i	1.07164	+	0.306761i
$976$	1.39349e7			0.468250
$977$		−	3.61680e7i		−	1.21224i	−0.795374	−	0.606119i	$-0.792726\pi$
$977$		−	3.61680e7i		−	1.21224i	0.795374	−	0.606119i	$-0.207274\pi$
$978$		−	2.88523e7i		−	0.964568i
$979$	−2.36558e7			−0.788825
$980$	452747.	−	3.22678e6i	0.0150588	−	0.107326i
$981$	−5.72263e6			−0.189855
$982$		−	2.17080e7i		−	0.718359i
$983$			4.73431e7i			1.56269i	0.624100	+	0.781344i	$0.285466\pi$
$983$			4.73431e7i			1.56269i	−0.624100	+	0.781344i	$0.714534\pi$
$984$	−3.12898e6			−0.103019
$985$	1.39047e7	+	1.95096e6i	0.456638	+	0.0640705i
$986$	−1.89258e7			−0.619958
$987$		−	4.96862e6i		−	0.162347i
$988$			2.32995e7i			0.759372i
$989$	−3.29666e6			−0.107173
$990$	2.19345e6	+	307762.i	0.0711280	+	0.00997992i
$991$	5.32159e7			1.72130			0.860651	−	0.509195i	$-0.170057\pi$
$991$	5.32159e7			1.72130			0.860651	+	0.509195i	$0.170057\pi$
$992$			6.20909e6i			0.200331i
$993$		−	4.60394e7i		−	1.48169i
$994$	2.00611e6			0.0644003
$995$	−2.43418e6	+	1.73487e7i	−0.0779463	+	0.555532i
$996$	−2.28532e7			−0.729960
$997$		−	8.63822e6i		−	0.275224i	−0.990486	−	0.137612i	$-0.956057\pi$
$997$		−	8.63822e6i		−	0.275224i	0.990486	−	0.137612i	$-0.0439427\pi$
$998$		−	3.83456e7i		−	1.21868i
$999$	4.40556e7			1.39665

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.6.b.a.139.23	yes	26
5.4	even	2	inner	230.6.b.a.139.4	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.6.b.a.139.4	✓	26	5.4	even	2	inner
230.6.b.a.139.23	yes	26	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	230.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+4.00000i q^{2} +13.9839i q^{3} -16.0000 q^{4} +(-7.76744 + 55.3594i) q^{5} -55.9357 q^{6} +114.735i q^{7} -64.0000i q^{8} +47.4501 q^{9} +(-221.438 - 31.0698i) q^{10} -208.757 q^{11} -223.743i q^{12} +757.151i q^{13} -458.938 q^{14} +(-774.142 - 108.619i) q^{15} +256.000 q^{16} +1028.75i q^{17} +189.800i q^{18} -1923.29 q^{19} +(124.279 - 885.751i) q^{20} -1604.44 q^{21} -835.026i q^{22} +529.000i q^{23} +894.971 q^{24} +(-3004.33 - 860.003i) q^{25} -3028.60 q^{26} +4061.63i q^{27} -1835.75i q^{28} +4599.22 q^{29} +(434.477 - 3096.57i) q^{30} +6063.57 q^{31} +1024.00i q^{32} -2919.23i q^{33} -4115.01 q^{34} +(-6351.64 - 891.194i) q^{35} -759.201 q^{36} -10846.8i q^{37} -7693.15i q^{38} -10587.9 q^{39} +(3543.00 + 497.116i) q^{40} -3496.19 q^{41} -6417.75i q^{42} +6231.87i q^{43} +3340.11 q^{44} +(-368.566 + 2626.81i) q^{45} -2116.00 q^{46} +3096.80i q^{47} +3579.88i q^{48} +3642.99 q^{49} +(3440.01 - 12017.3i) q^{50} -14386.0 q^{51} -12114.4i q^{52} -10267.9i q^{53} -16246.5 q^{54} +(1621.51 - 11556.6i) q^{55} +7343.01 q^{56} -26895.1i q^{57} +18396.9i q^{58} -5297.34 q^{59} +(12386.3 + 1737.91i) q^{60} +54433.0 q^{61} +24254.3i q^{62} +5444.16i q^{63} -4096.00 q^{64} +(-41915.5 - 5881.13i) q^{65} +11676.9 q^{66} -39973.0i q^{67} -16460.0i q^{68} -7397.49 q^{69} +(3564.78 - 25406.6i) q^{70} -4371.19 q^{71} -3036.80i q^{72} +25765.2i q^{73} +43387.2 q^{74} +(12026.2 - 42012.4i) q^{75} +30772.6 q^{76} -23951.6i q^{77} -42351.8i q^{78} +44456.9 q^{79} +(-1988.47 + 14172.0i) q^{80} -45267.1 q^{81} -13984.7i q^{82} -102141. i q^{83} +25671.0 q^{84} +(-56951.1 - 7990.77i) q^{85} -24927.5 q^{86} +64315.1i q^{87} +13360.4i q^{88} +113318. q^{89} +(-10507.2 - 1474.26i) q^{90} -86871.4 q^{91} -8464.00i q^{92} +84792.4i q^{93} -12387.2 q^{94} +(14939.0 - 106472. i) q^{95} -14319.5 q^{96} -10460.6i q^{97} +14571.9i q^{98} -9905.51 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 416 q^{4} - 30 q^{5} - 72 q^{6} - 1400 q^{9} + 80 q^{10} - 1314 q^{11} + 808 q^{14} + 1280 q^{15} + 6656 q^{16} + 6630 q^{19} + 480 q^{20} - 10060 q^{21} + 1152 q^{24} - 10470 q^{25} - 376 q^{26}+ \cdots + 523850 q^{99}+O(q^{100}) \) 26 * q - 416 * q^4 - 30 * q^5 - 72 * q^6 - 1400 * q^9 + 80 * q^10 - 1314 * q^11 + 808 * q^14 + 1280 * q^15 + 6656 * q^16 + 6630 * q^19 + 480 * q^20 - 10060 * q^21 + 1152 * q^24 - 10470 * q^25 - 376 * q^26 + 16084 * q^29 - 6200 * q^30 + 418 * q^31 + 3320 * q^34 - 3160 * q^35 + 22400 * q^36 + 71296 * q^39 - 1280 * q^40 - 35826 * q^41 + 21024 * q^44 - 83960 * q^45 - 55016 * q^46 + 53532 * q^49 - 20800 * q^50 - 25430 * q^51 + 98736 * q^54 - 110390 * q^55 - 12928 * q^56 + 126992 * q^59 - 20480 * q^60 - 63662 * q^61 - 106496 * q^64 - 88520 * q^65 - 18664 * q^66 - 9522 * q^69 - 116520 * q^70 - 106514 * q^71 + 183536 * q^74 - 44200 * q^75 - 106080 * q^76 + 324676 * q^79 - 7680 * q^80 - 170702 * q^81 + 160960 * q^84 + 120780 * q^85 - 42768 * q^86 + 465200 * q^89 + 61360 * q^90 - 468838 * q^91 + 107152 * q^94 + 309670 * q^95 - 18432 * q^96 + 523850 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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